1. Field of the Invention
The present application is in the field of optical fibers for propagating light, and more particularly is in the field of photonic-bandgap fibers having a hollow core, or a core with a refractive index lower than the cladding materials.
2. Description of the Related Art
Photonic-bandgap fibers (PBFs) have attracted great interest in recent years due to their unique advantages over conventional fibers. In particular, the propagation loss in an air-core PBF is not limited by the core material, and it is expected that the propagation loss can be exceedingly low. The nonlinear effects in an air-core PBF are very small, and in certain PBFs, the core can be filled with liquids or gases to generate the desired light-matter interaction. Numerous new applications enabled by these advantages have been demonstrated recently. Such applications are described, for example, in Burak Temelkuran et al., Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission, Nature, Vol. 420, 12 Dec. 2002, pages 650–653; Dimitri G. Ouzounov et al., Dispersion and nonlinear propagation in air-core photonic band-gap fibers, Proceedings of Conference on Laser and Electro-Optics (CLEO) 2003, Baltimore, USA, 1–6 Jun. 2003, paper CThV5, 2 pages; M. J. Renn et al., Laser-Guided Atoms in Hollow-Core Optical Fibers, Physical Review Letters, Vol. 75, No. 18, 30 Oct. 1995, pages 3253–3256; F. Benabid et al., Particle levitation and guidance in hollow-core photonic crystal fiber, Optics Express, Vol. 10, No. 21, 21 Oct. 2002, pages 1195–1203; and Kazunori Suzuki et al., Ultrabroad band white light generation from a multimode photonic bandgap fiber with an air core, Proceedings of Conference on Laser and Electro-Optics (CLEO) 2001, paper WIPD1-11, pages 24–25, which are hereby incorporated herein by reference.
Calculations of selected properties of the fundamental mode of the PBFs have also been reported in, for example, R. F. Cregan et al., Single-Mode Photonic Band Gap Guidance of Light in Air, Science, Vol. 285, 3 Sep. 1999, pages 1537–1539; Jes Broeng et al., Analysis of air guiding photonic bandgap fibers, Optics Letters, Vol. 25, No. 2, Jan. 15, 2000, pages 96–98; and Jes Broeng et al., Photonic Crystal Fibers: A New Class of Optical Waveguides, Optical Fiber Technology, Vol. 5, 1999, pages 305–330, which are hereby incorporated herein by reference.
Surface modes, which do not exist in conventional fibers, are defect modes that form at the boundary between the air core and the photonic-crystal cladding. Surface modes can occur when an infinite photonic crystal is abruptly terminated, as happens for example at the edges of a crystal of finite dimensions. Terminations introduce a new set of boundary conditions, which result in the creation of surface modes that satisfy these conditions and are localized at the termination. See, for example, F. Ramos-Mendieta et al., Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane, Physical Review B, Vol. 59, No. 23, 15 Jun. 1999, pages 15112–15120, which is hereby incorporated herein by reference.
In a photonic crystal, the existence of surface modes depends strongly on the location of the termination. See, for example, A. Yariv et al., Optical Waves in Crystals: Propagation and Control of Laser Radiation, John Wiley & Sons, New York, 1984, pages 209–214, particularly at page 210; and J. D. Joannopoulos et al., Photonic Crystals: Molding the flow of light, Princeton University Press, Princeton, N.J., 1995, pages 54–77, particularly at page 73; which are hereby incorporated herein by reference; and also see, for example, F. Ramos-Mendieta et al., Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane, cited above. For example, in photonic crystals made of dielectric rods in air, surface modes are induced only when the termination cuts through rods. A termination that cuts only through air is too weak to induce surface modes. See, for example, J. D. Joannopoulos et al., Photonic Crystals: Molding the flow of light, cited above.
Unless suitably designed, a fiber will support many surface modes. Recent demonstrations have shown that surface modes play a particularly important role in air-core PBFs, and mounting evidence indicates that surface modes impose serious limitations in air-core photonic-bandgap fibers by contributing to propagation losses. See, for example, K. Saitoh et al., Air-core photonic band-gap fibers: the impact of surface modes, Optics Express, Vol. 12, No. 3, February 2004, pages 394–400; Douglas C. Allan et al., Surface modes and loss in air-core photonic band-gap fibers, in Photonic Crystals Materials and Devices, A. Adibi et al. (eds.), Proceedings of SPIE, Vol. 5000, 2003, pages 161–174; Wah Tung Lau et al., Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs, Applied Physics Letters, Vol. 81, No. 21, 18 Nov. 2002, pages 3915–3917; Dirk Müller et al., Measurement of Photonic Band-gap Fiber Transmission from 1.0 to 3.0 μm and Impact of Surface Mode Coupling, Proceedings of Conference on Laser and Electro-Optics (CLEO) 2003, Baltimore, USA, 1–6 Jun. 2003, paper QTuL2, 2 pages; Hyang Kyun Kim et al., Designing air-core photonic-bandgap fibers free of surface modes, IEEE Journal of Quantum Electronics, Vol. 40, No. 5, May 2004, pages 551–556; and Michel J. F. Digonnet et al., Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers, Optics Express, Vol. 12, No. 9, May 2004, pages 1864–1872, which are hereby incorporated herein by reference. Also see, for example, J. D. Joannopoulos et al., Photonic Crystals: Molding the flow of light, cited above; A. Yariv et al., Optical Waves in Crystals: Propagation and Control of Laser Radiation, cited above; and F. Ramos-Mendieta et al., Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane, cited above.
In contrast to surface modes, a core mode (e.g., a fundamental core mode) of an air-core PDF without a silica core ring is one in which the peak of the mode intensity is located in the core. In most cases, most of the energy will also be contained within the air core. The propagation constants of surface modes often fall close to or can even be equal to the propagation constant of the fundamental core mode. See, for example, K. Saitoh et al., Air-core photonic band-gap fibers: the impact of surface modes, Douglas C. Allan et al., Surface modes and loss in air-core photonic band-gap fibers, in Photonic Crystals Materials and Devices, and Dirk Müller et al., c Measurement of Photonic Band-gap Fiber Transmission from 1.0 to 3.0 μm and Impact of Surface Mode Coupling, which are cited above.
The fundamental core mode generally couples quite strongly to one or more of these surface modes by a resonant coupling mechanism or a nearly-resonant coupling mechanism. Such coupling may be caused, for example, by random (e.g., spatial) perturbations in the fiber index profile or cross-section. Since surface modes are inherently lossy due to their high energy density in the dielectric of the fiber, such coupling is a source of propagation loss. Furthermore, since surface modes occur across the entire bandgap, no portion of the available spectrum is immune to this loss mechanism. Recent findings have demonstrated that surface modes are a cause of the reduced transmission bandwidth in a 13-dB/km air-core PBF manufactured by Corning. See, for example, N. Venkataraman et al., Low loss (13 dB/km) air core photonic band-gap fibre, Proceedings of European Conference on Optical Communication, ECOC 2002, Copenhagen, Denmark, PostDeadline Session 1, PostDeadline Paper PD1.1, Sep. 12, 2002; and C. M. Smith, et al., Low-loss hollow-core silica/air photonic bandgap fibre, Nature, Vol. 424, No. 6949, 7 Aug. 2003, pages 657–659, which are incorporated by reference herein. This effect is believed to be the source of the remaining loss (approximately 13 dB/km) in this air-core photonic-bandgap fiber. See, for example, Douglas C. Allan et al, Photonic Crystals Materials and Devices, cited above. Understanding the physical origin of surface modes and identifying fiber configurations that are free of such modes across the entire bandgap is therefore of importance in the ongoing search for low-loss PBFs.